Peak level of play (Federer, Nadal, Djokovic & Co.)

The longevity debate we’ve been having touches on the issue of peak level of play, but only indirectly. The reasons we give for Federer’s decline do imply something about his peak level of play: if even a GOAT level player has genuinely good reasons, in today’s game, why he would fall behind his main rivals at around the age of 30, then that supports the argument that his peak level was genuinely GOAT level. If, on the other hand, there is no good reason why a 30-year-old should be falling behind his rivals in today’s game, then that lends weight to the argument that Federer is losing now because he is encountering tough rivals for the first time and his peak level was never GOAT level to begin with.

But all that was an indirect way to talk about peak level. Match stats can directly illustrate peak level of play, and I want to list those that I have gathered for Federer, Nadal and Djokovic.

The stats still have to be interpreted, but this, at least, is a direct measurement of level of play.

The most common stats used today to illustrate level of play are winners and unforced errors. Subtracting the errors from the winners, we get winner/error differentials, which can be useful. But that method has one large drawback, in that it only counts the unforced errors. The forced errors – which are almost never reported – are nowhere to be seen, and often they tell a different story.

Basically, in tennis you want to be as aggressive as possible while making as few errors as possible. That's what the Aggressive Margin measures. It counts the points that you win aggressively -- either by striking clean winners or by forcing your opponent into errors -- and compares that with how many points you lost by making unforced errors.

To put it most simply, if you win 25% of the all the points played in a match through aggressive plays – either by striking clean winners or by forcing your opponent into errors – and you lose 10% of all the points played in the match through unforced errors of your own, then your Aggressive Margin is 15%.

To have a high Aggressive Margin does not mean that you have to be what we normally think of as "an aggressive player." A guy who makes relatively few winners and few errors, like Nadal, can have just as high an Aggressive Margin as a guy who makes a ton of winners and errors. What matters is whether you can win points but not pay too high a cost in errors. Whoever does better at that balancing act has the higher Aggressive Margin and is almost always the winner of the match.

Over the years I’ve collected official stats for many matches, from which I’ve calculated Aggressive Margins. I have stats for all of the GS finals played by Federer, Nadal, Djokovic and Murray, against each other or against any player. I have stats for dozens more of their matches, and stats for many other players as well.

NOTE: the highest Aggressive Margins tend to occur on grass. The slower the surface, the more difficult it is to hit winners or to force errors from your opponents.

The highest Aggressive Margin I’ve ever calculated belongs to John McEnroe in the 1984 Wimbledon final: 52.8%. That does not automatically mean that his performance was the best of all time. Stats can’t be used that literally; and it’s a matter of judgment whether 52.8% against an aging Jimmy Connors is as impressive as some other performances we could name.

Any additional stats, comments, questions, arguments and corrections are most welcome.

This run of 3 matches might be where the Aggressive Margin method is at its most impressive. All statistical methods have pros and cons, but whatever the drawbacks of the Aggressive Margin method, it tracks very well with the scorelines of these matches.

What I mean is that every once in a while you see a stat that does not reflect the result of the match, or reflects it poorly -- like when the loser of the match has a higher winner/error differential than his opponent. Or in other cases the victor does have a better differential, but not by the margin reflected in the scoreline.

But the AM method reflects the results and scorelines of these 3 matches very well. In the 2008 match, Nadal was at 31.5% and Federer at 30.3%. Nadal was just 1.2% "better" than Federer, which reflects the fact that he barely won the match 9-7 in the fifth.

In 2007 Federer is at 33.1% and Nadal at 31.0%. The difference there is 2.1%. That looks like a little bit more of a margin of victory, though not much: and it was still a close five-set battle but Federer pulled through by a more comfortable 6-2 margin in the fifth.

In 2006 Federer is at 30.5% and Nadal at 22.4%. That looks like a comfortable victory, but not a blowout: and in fact Federer took that match in four sets. Nadal's performance there is the only one in the three matches not around the 30% level, though his figure of 22.4% is a bit deceptive because it partly reflects his very poor start in that match (he was bageled in the first set, while making a battle of the next three sets).

The AM method will not necessarily work so well with other matches, of course. But the fact that it tracks so well with the scorelines of these 3 matches is a plus for using this method.

Great stuff. Thanks for all the work you've put into this abmk and (especially) krosero.

This measure certainly captures a lot of the important aspects of a match, but doesn't track all that well with my subjective judgements of player performance in the match (though it's doesn't do too badly either). Maybe it's the inflated stats on grass that are messing with my intuitions here.

Dont know about this method, although i appreciate the input by Krosero. Following the results, Federer had his peak level mostly 2008-12, with the Roddick matches at Wim 2003-5 in between. It is somewhat corresponding with my impressions, that Federer played more serve and volley against Roddick and Philippoussis 2003 at Wim.
Tennis level is always relative to opponent, surface and playing style. I would assume, that most players hit more winners on grass, that one player plays more for winners than another, who is defending better and basically tries to play one more ball back, to win; that is is more difficult to hit winners against fast players than against slower ones and so on.

Dont know about this method, although i appreciate the input by Krosero. Following the results, Federer had his peak level mostly 2008-12, with the Roddick matches at Wim 2003-5 in between. It is somewhat corresponding with my impressions, that Federer played more serve and volley against Roddick and Philippoussis 2003 at Wim.

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what makes you think that federer had his peak level b/w 2008 and 2012 ?

that's just from the list of matches krosero has. it isn't a comprehensive list by any means ...

Tennis level is always relative to opponent, surface and playing style. I would assume, that most players hit more winners on grass, that one player plays more for winners than another, who is defending better and basically tries to play one more ball back, to win; that is is more difficult to hit winners against fast players than against slower ones and so on.

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yeah, which is why I said federer's performance vs nadal @ the YEC in 2011 stands out, it was on a medium surface against an elite defender ....

Do you feel aggressive margins are more important or aggressive ratios?

One problem I have is let's say a player is very aggressive as for example Rod Laver. Laver faces a ball machine like Bjorn Borg, well Laver is probably going to hit less winners and make more errors. Obviously the surface has to be taken into account.

I think from some of your examples that is why I believe Federer is so rarely upset by players outside of the top few His forehand is almost the equivalent of a powerful volley putaway by today's standards. When he gets a short ball it is rare players outside of Nadal, Djokovic and Murray that they had a chance to win the point. Just a theory but a theory from observation.

Nadal, Murray and Djokovic don't have the same type of putaway forehand that I believe Federer has.

Over the course of a year or a few years, if all the matches were charted I can easily see this as a super valuable statistic. Great job.

One problem I have is let's say a player is very aggressive as for example Rod Laver. Laver faces a ball machine like Bjorn Borg, well Laver is probably going to hit less winners and make more errors. Obviously the surface has to be taken into account.

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yeah, the surface matters a lot here , which is why it'd be better to arrange it by the surface ....

by aggressive ratio you mean : no of points won by a player through forcing/total number of points in the match

where no of points won by forcing = winners+errors forced from opponent ?

yeah, the surface matters a lot here , which is why it'd be better to arrange it by the surface ....

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I mean if a player hits 45 winners and has 15 errors, that would be a 3 to 1 ratio. Another player may hit 15 winners and have only 5 errors but has the same 3 to 1 ratio.

If you do plus-minus the first guy is far better at plus 30 than the second guy at plus 10.

I think ratio may be better.

One other thing we should considering is normalizing the information for the eras. They do that in the National Football League and Major League Baseball all the time. I wrote an article for a well known NFL magazine a few years ago normalizing information on the teams stats of NFL teams from the 1940's onward to the present. The results were in line with the relative dominance of the teams. In the wood era there were far more errors than winners. We should perhaps consider ratios for the different eras also. So era like the 1970's and 1980's had a mix of different racquets and equipment. So used wood into the 1980's and switched to a more modern racquet. Some have argue that Chris Evert was at a huge disadvantage against Martina Navratilova for a while when Navratilova was beat Evert all the time because Evert used wood and Navratilova the most modern racquet. One Evert switched to a modern racquet, it was competitive against.

Some statisticians have used standard deviations as a way of normalizing information. We obviously don't have this information available but it would be wonderful if some researcher was able to find as many matches as possibly to get a large statistical sample.

federer won 52 points in that match, they have him @ 31 winners, nadal at 7 UEs, therefore federer only forced 14 errors from nadal ?

he had 31 winners , but forced only 14 errors from nadal? :-?

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Yes those official stats are messed up, but fortunately they don't have an impact on the AM. As long as the unforced errors can be trusted -- and they do look ok -- then the remaining points can be regarded as either forcing points or as clean winners, without worrying about how many exactly were clean winners. That's the problem with the official stats: the figures that they have for Winners are actually the number of points that each player won, in total, on serve (ie, Federer won 31 points on his own serve, Nadal won 46 on his own).

In 2007 the RG site also had a problem counting Winners, and I don't know how the Winners were calculated that year. Fortunately, again, it doesn't have an impact on the AM, so long as the Unforced Errors look reliable, which they do.

Having actually watched those 2 matches , I feel sampras played a tad bit better in the stich match ( I can see the sampras fans angrily shouting here ! ) - especially returning wise ...

don't have the stats with me for either of the matches now , but I feel sampras' AM would be better in the 92 QF ....

want to see how many of those who watched both those matches agree with me !

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The official Wimbledon stats in '99 have Unforced Errors that are completely unreliable. Those figures look like the total number of errors of every kind, forced and unforced. They've got Sampras at 51 unforced errors. NBC put Sampras at only 22, which looks right. Unfortunately I don't know the UE count that NBC had for Agassi, so AM's can't be calculated.

To have a high Aggressive Margin does not mean that you have to be what we normally think of as "an aggressive player." A guy who makes relatively few winners and few errors, like Nadal, can have just as high an Aggressive Margin as a guy who makes a ton of winners and errors. What matters is whether you can win points but not pay too high a cost in errors. Whoever does better at that balancing act has the higher Aggressive Margin and is almost always the winner of the match.

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I think your analysis is quite interesting, but I disagree with the bolded statement. It also depends on what you define as peak. Are we referring to a period of time? ie. 2005-2006 for Federer. Or are we referring to peak levels in certain matches? If you are referring to peak level in certain matches, then that is fine, but players like Berdych, Tsonga and Del Potro will have very high margins for certain matches. If we are drawing a conclusion from the sample about a period of time, then there are some points to consider (see the reasons below).

To clarify, I don't think there is anything wrong with biasing towards more aggressive players since you are effectively trying to measure how aggressive a player relative to his/her errors.

Reasons for bias towards aggressive players:

1) Aggressive players play high risk high reward tennis, over the wide spread of matches played throughout one's career, they are more likely to have wins with a high margin of aggressively won points over unforced errors, than their defensive counterparts. This can cause skewed results. For example, let's say Isner and Nadal play 150 matches against the field during the defined "peak period" (150 matches is roughly 2-2.5 years).

Isner -Being a risky player, Isner always has a high winner/forced error, high unforced ratio. Over his 150 matches, his aggressive margin is 10%, because of his high unforced error count. However, he gets on fire 10 of the 150 (6.67%) matches he played, and has a high margin of 50% for his top 10 scores, supposedly representing his peak period.

Nadal -Being a defensive player, Nadal has a lower winner, lower unforced ratio. Over his 150 matches, his aggressive margin is 25%. Because of his steady play, this 25% held true for each of his 200 matches. Thus, his top 10 matches also average 25%, which is 1/2 of what Isner achieved in his top 10 matches.

This clearly does award players that "we normally think of as "an aggressive player."

To reduce this bias, perhaps one can define a peak period, say all matches in 2005 and 2006, and then select a random sample of matches to calculate the aggressive margin, rather than selecting the top aggressive margins over a large amount of years.

2) Also, using a direct calculation of % points won aggressively subtracting the % points lost due to unforced errors will be advantageous for the aggressive player.

ie: In a match, Isner won 50% of points aggressively, but lost 30% of points due to unforced errors. The aggressive margin is 20%. The RATIO is 50/30 = 1.67 times more aggressively won points than errors.

Nadal won 15% of points aggressively, but lost 2% of points due to unforced errors. The aggressive margin is 13%. The RATIO is 7.5 times more aggressively won points than errors.

Which statistic is actually more impressive in terms of "balancing aggressive shots and errors" as you said you were trying to find out from the stats?

I had Becker with 7. I know that's unofficial, but I'm curious what the AM would be in that match. That goes for any of our stats where we calculated UE's(Laver-Ashe etc)
You could just mention that the AM was calculated with unofficial stats when posting some of these(I doubt Laver ever played a match where officials were calculating winners/ue's, may as well use ours just for fun)

I guess the winner # isn't really necessary in calculating any AM's, just the UE count for both players.

I mean if a player hits 45 winners and has 15 errors, that would be a 3 to 1 ratio. Another player may hit 15 winners and have only 5 errors but has the same 3 to 1 ratio.

If you do plus-minus the first guy is far better at plus 30 than the second guy at plus 10.

I think ratio may be better.

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In a nutshell, I think the Aggressive Margin is better than ratios, and I'll try to explain why as succinctly as I can.

Just like you, I have always suspected that ratios might be better, just from thinking about the problem the way you just laid it out. But when I actually look at the stats I've collected, I find that plus-minus differentials do not put Nadal at a disadvantage. To the contrary, in matches in which he plays far more aggressive players and the match is a close one (we have to assume it's close, to keep things fair), Nadal tends to have better plus-minus differentials than the more aggressive players.

The best example I know is when he beat Verdasco at the 2009 AO. The match was extremely close (Nadal won 193 points, Verdasco 192), so it's a good example of two players who were more or less equal in level of play. Verdasco hit nearly twice as many winners as Nadal did (95 to 52). So it's a perfect example of Nadal facing a much more aggressive player.

But the plus-minus methods do not put him at a disadvantage. Nadal's official winner/error differential was +27, compared to only +19 for Verdasco. So that method treats him fairly: in fact it exaggerates his quality of play, because he didn't win the match by such a large margin. The Aggressive Margin represents the match most accurately: Nadal's AM was 23.9%, Verdasco's 23.6%.

The same occurs in the final that year, between Nadal and Federer (another extremely close match decided by a 1-point edge). Federer usually hits more winners than Nadal. In this match Federer had 71 winners, to Nadal's 50. But Nadal is the one with a better winner/error differential: Federer is at only +7, while Nadal is at +9.

In other words, when Nadal wins matches, it's because he's keeping his unforced errors down extraordinarily low. That's why he can win the winner/error differential contest.

Intuitively, I would have thought that Nadal, like you wrote above, has 15 winners and 5 ue, while his opponent, playing at an equal level, has 45 winners and 15 unforced errors. But the guy with those low numbers will not win that match: he's won 15 points with winners, and 15 points with his opponent's errors. He's got a total of 30 points. Nadal's opponent, on the other hand, has 45 winners + 5 ue from Nadal: a total of 50 points. Nadal's opponent will almost surely beat him, if the ratios advance like this.

What actually happens when different styles clash is that, all things being equal, Nadal will have 15 winners and 15 unforced errors, while Isner will have 50 winners and 50 unforced errors. Either man can win that match.

If the match is of less quality, then Nadal will have 15 winners and 25 errors (-10), while Isner will have 50 winners and 60 errors (-10).

I have many more examples of how Nadal actually looks very good when simple plus-minus methods are used. In the 2006 Wimbledon final, which Nadal lost to Federer in four sets, Nadal had a better winner/error differential than Federer did (+16 compared to +11). That's because something different is going on with the missing category of FORCED errors: but you see what I mean. Plus/minus differentials are often very good for Nadal.

When Nadal lost to Soderling in four sets at RG, again he had a better differential than the man he lost to: +5 compared to +2. And that's an extreme example of clashing styles: Soderling hit almost twice as many winners as Nadal did (61 to 33). Yet Nadal comes out with the better differential.

And in that 2006 Wimbledon final, the AM again is the more accurate method: Federer has 30.5%, Nadal 22.4%.

Soderling, when he upset Federer at RG in 2010, outstripped Roger in winners (49-40). But once again the guy with fewer winners somehow ended up with the better winner/error differential: Soderling's was only +7, while Federer's was +13. Federer kept his UEs down very low (though that was not enough to win him the match).

I do know of one example where a plus/minus method puts Nadal at a disadvantage. When he beat Berdych in their Wimbledon final in 2010 (a straight set match), his winner/error differential was only +8, while Berdych was +10.

So in that case, Nadal's level of play is not represented correctly. But the Aggressive Margin method gets it right: Nadal has 32.2%, Berdych 23.4%.

The odd thing about that example is that we all think of Berdych as having a more aggressive style than Nadal. But Nadal actually hit more winners than Berdych in that match (29-27). And Nadal made more unforced errors than Berdych (21-17). Totally surprising, but that's why Berdych's differentials turned out better than Nadal's.

I thought Nadal really went for his shots in that match. He did it in a controlled way, as always, but he went for them.

It seems that simple winner/error differentials can actually favor the guy who is more patient (or consistent, or cautious), because that guy can keep his unforced errors down extraordinarily low and can therefore come out with a favorable winner/error differential.

The Aggressive Margin method does not have these drawbacks, partly because it considers all the points in a match (forced errors as well as unforced errors).

Thanks for this particular question, PC1, it has helped me to learn a lot more about this method; and it's fun talking about these matches. Like I said, I thought about this ratio problem exactly as you did -- until I checked the differentials I'd gathered over the years.

Another great example of clashing styles: 1988 USO final between Wilander and Lendl. Wilander had approximately 35 winners and 35 errors. Lendl was at about 85 winners and 85 unforced errors. The match went down to the wire, 6-4 in the fifth.

I'm taking those stats from memory, but yes, each player's winners and errors were almost exactly equal. Only the totals between the players differed, and by a lot: you can't get a greater contrast in styles than those two men.

Wilander, despite being nowhere near as aggressive as Lendl, is represented accurately in the Aggressive Margins. He had 13.8%, Lendl 12.2%.

I had Becker with 7. I know that's unofficial, but I'm curious what the AM would be in that match. That goes for any of our stats where we calculated UE's(Laver-Ashe etc)
You could just mention that the AM was calculated with unofficial stats when posting some of these(I doubt Laver ever played a match where officials were calculating winners/ue's, may as well use ours just for fun)

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If you add those 7 to Becker's 15 df's, his total UE would be 22. Sampras had 7 UE of every kind (all 7 were DF's), per official sources including NBC.

So, if Becker has 22 UE's, Sampras' AM is 44.3%, Becker's 32.1%.

If you give Becker more than 22, Sampras' AM would go down.

If Becker goes down below 22, Sampras' AM would rise. Becker has at least 15 UE's (his df's), so Sampras' ceiling in this match would be 47.2%.

I would be wary of comparing AM's across eras if we go back as far as Laver. (Even comparing against the Sampras era could be problematic). But sure, it's worth doing.

Here's a question: are service winners included in the opponents forced error column? IMO, this method would be more accurate if serve-related stats are excluded in calculating the AM.

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The AM takes into account every point in the match, so quick answer is yes. The AM is calculated by taking the total number of points that a player won, and subtracting the points that he won through his opponent's unforced errors. The result, mathematically, must be the points that he won aggressively (his Aggressive Points), either through clean winners/aces or by forcing his opponent into errors.

The last step is to take those Aggressive Points and compare them to the same player's Unforced Errors. The final result is the Aggressive Margin.

I can't imagine how this method would be more accurate if service winners are excluded. It MIGHT become more accurate, in that case, if you're looking for levels of play apart from service. But I have doubts about that, because the serve is connected to everything. Not every point in tennis has a forehand, but every point has a serve.

Moose and I have seen matches in which winner/error differentials -- because they only use unforced errors -- give a distorted picture of the match. The loser will come away with a higher winner/error differential, for example. But the loser, in these examples, definitely lost more than 50% of all the points played (we know because we counted). That's how you know that the victor must have pulled ahead in the missing category of forced errors.

And when there is a large difference in the quality of two players' serves -- or a large difference in the quality of their returns -- one player will get a lot more free points by forcing errors on the return. Those errors are not aces, and not outright unreturnable serves, so they don't show up in the typical winner/error stats. But those errors often make the difference.

So I'm not sure what you're trying to isolate by taking out the serve. You might isolate something, but total level of play definitely has to include everything.

In a nutshell, I think the Aggressive Margin is better than ratios, and I'll try to explain why as succinctly as I can.

Just like you, I have always suspected that ratios might be better, just from thinking about the problem the way you just laid it out. But when I actually look at the stats I've collected, I find that plus-minus differentials do not put Nadal at a disadvantage. To the contrary, in matches in which he plays far more aggressive players and the match is a close one (we have to assume it's close, to keep things fair), Nadal tends to have better plus-minus differentials than the more aggressive players.

The best example I know is when he beat Verdasco at the 2009 AO. The match was extremely close (Nadal won 193 points, Verdasco 192), so it's a good example of two players who were more or less equal in level of play. Verdasco hit nearly twice as many winners as Nadal did (95 to 52). So it's a perfect example of Nadal facing a much more aggressive player.

But the plus-minus methods do not put him at a disadvantage. Nadal's official winner/error differential was +27, compared to only +19 for Verdasco. So that method treats him fairly: in fact it exaggerates his quality of play, because he didn't win the match by such a large margin. The Aggressive Margin represents the match most accurately: Nadal's AM was 23.9%, Verdasco's 23.6%.

The same occurs in the final that year, between Nadal and Federer (another extremely close match decided by a 1-point edge). Federer usually hits more winners than Nadal. In this match Federer had 71 winners, to Nadal's 50. But Nadal is the one with a better winner/error differential: Federer is at only +7, while Nadal is at +9.

In other words, when Nadal wins matches, it's because he's keeping his unforced errors down extraordinarily low. That's why he can win the winner/error differential contest.

Intuitively, I would have thought that Nadal, like you wrote above, has 15 winners and 5 ue, while his opponent, playing at an equal level, has 45 winners and 15 unforced errors. But the guy with those low numbers will not win that match: he's won 15 points with winners, and 15 points with his opponent's errors. He's got a total of 30 points. Nadal's opponent, on the other hand, has 45 winners + 5 ue from Nadal: a total of 50 points. Nadal's opponent will almost surely beat him, if the ratios advance like this.

What actually happens when different styles clash is that, all things being equal, Nadal will have 15 winners and 15 unforced errors, while Isner will have 50 winners and 50 unforced errors. Either man can win that match.

If the match is of less quality, then Nadal will have 15 winners and 25 errors (-10), while Isner will have 50 winners and 60 errors (-10).

I have many more examples of how Nadal actually looks very good when simple plus-minus methods are used. In the 2006 Wimbledon final, which Nadal lost to Federer in four sets, Nadal had a better winner/error differential than Federer did (+16 compared to +11). That's because something different is going on with the missing category of FORCED errors: but you see what I mean. Plus/minus differentials are often very good for Nadal.

When Nadal lost to Soderling in four sets at RG, again he had a better differential than the man he lost to: +5 compared to +2. And that's an extreme example of clashing styles: Soderling hit almost twice as many winners as Nadal did (61 to 33). Yet Nadal comes out with the better differential.

And in that 2006 Wimbledon final, the AM again is the more accurate method: Federer has 30.5%, Nadal 22.4%.

Soderling, when he upset Federer at RG in 2010, outstripped Roger in winners (49-40). But once again the guy with fewer winners somehow ended up with the better winner/error differential: Soderling's was only +7, while Federer's was +13. Federer kept his UEs down very low (though that was not enough to win him the match).

I do know of one example where a plus/minus method puts Nadal at a disadvantage. When he beat Berdych in their Wimbledon final in 2010 (a straight set match), his winner/error differential was only +8, while Berdych was +10.

So in that case, Nadal's level of play is not represented correctly. But the Aggressive Margin method gets it right: Nadal has 32.2%, Berdych 23.4%.

The odd thing about that example is that we all think of Berdych as having a more aggressive style than Nadal. But Nadal actually hit more winners than Berdych in that match (29-27). And Nadal made more unforced errors than Berdych (21-17). Totally surprising, but that's why Berdych's differentials turned out better than Nadal's.

I thought Nadal really went for his shots in that match. He did it in a controlled way, as always, but he went for them.

It seems that simple winner/error differentials can actually favor the guy who is more patient (or consistent, or cautious), because that guy can keep his unforced errors down extraordinarily low and can therefore come out with a favorable winner/error differential.

The Aggressive Margin method does not have these drawbacks, partly because it considers all the points in a match (forced errors as well as unforced errors).

Thanks for this particular question, PC1, it has helped me to learn a lot more about this method; and it's fun talking about these matches. Like I said, I thought about this ratio problem exactly as you did -- until I checked the differentials I'd gathered over the years.

Another great example of clashing styles: 1988 USO final between Wilander and Lendl. Wilander had approximately 35 winners and 35 errors. Lendl was at about 85 winners and 85 unforced errors. The match went down to the wire, 6-4 in the fifth.

I'm taking those stats from memory, but yes, each player's winners and errors were almost exactly equal. Only the totals between the players differed, and by a lot: you can't get a greater contrast in styles than those two men.

Wilander, despite being nowhere near as aggressive as Lendl, is represented accurately in the Aggressive Margins. He had 13.8%, Lendl 12.2%.

If you add those 7 to Becker's 15 df's, his total UE would be 22. Sampras had 7 UE of every kind (all 7 were DF's), per official sources including NBC.

So, if Becker has 22 UE's, Sampras' AM is 44.3%, Becker's 32.1%.

If you give Becker more than 22, Sampras' AM would go down.

If Becker goes down below 22, Sampras' AM would rise. Becker has at least 15 UE's (his df's), so Sampras' ceiling in this match would be 47.2%.

I would be wary of comparing AM's across eras if we go back as far as Laver. (Even comparing against the Sampras era could be problematic). But sure, it's worth doing.

Exactly.

The AM takes into account every point in the match, so quick answer is yes. The AM is calculated by taking the total number of points that a player won, and subtracting the points that he won through his opponent's unforced errors. The result, mathematically, must be the points that he won aggressively (his Aggressive Points), either through clean winners/aces or by forcing his opponent into errors.

The last step is to take those Aggressive Points and compare them to the same player's Unforced Errors. The final result is the Aggressive Margin.

I can't imagine how this method would be more accurate if service winners are excluded. It MIGHT become more accurate, in that case, if you're looking for levels of play apart from service. But I have doubts about that, because the serve is connected to everything. Not every point in tennis has a forehand, but every point has a serve.

Moose and I have seen matches in which winner/error differentials -- because they only use unforced errors -- give a distorted picture of the match. The loser will come away with a higher winner/error differential, for example. But the loser, in these examples, definitely lost more than 50% of all the points played (we know because we counted). That's how you know that the victor must have pulled ahead in the missing category of forced errors.

And when there is a large difference in the quality of two players' serves -- or a large difference in the quality of their returns -- one player will get a lot more free points by forcing errors on the return. Those errors are not aces, and not outright unreturnable serves, so they don't show up in the typical winner/error stats. But those errors often make the difference.

So I'm not sure what you're trying to isolate by taking out the serve. You might isolate something, but total level of play definitely has to include everything.

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Interesting how in the 1988 US Open Lendl was deemed to be more aggressive but I understand that's a part of his more powerful stroking style. We often (not me by the way)relate aggressive play to rushes to the net. If I recall Wilander rushed the net far more often. Another question does occur to me, net rushes often forces passing shots errors, can we statistically take this into account?

Interesting how in the 1988 US Open Lendl was deemed to be more aggressive but I understand that's a part of his more powerful stroking style. We often (not me by the way)relate aggressive play to rushes to the net. If I recall Wilander rushed the net far more often. Another question does occur to me, net rushes often forces passing shots errors, can we statistically take this into account?

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You know, that's my favorite match, yet in all this talk about aggressive play I had actually forgotten about Wilander's net rushes. We typically think of aggression as hitting winners, but in past eras "aggressive" meant rushing the net! Absolutely right.

Wilander had, I think, 131 approaches, Lendl 77. Lendl was aggressive, too, by that measure -- more than most players today. But Wilander was twice as willing to come forward.

That was part of the reason that Lendl hit so many more winners: Wilander forced him to hit a ton of passing shots.

You ask if we can take passing shot errors into account. Rushing the net and forcing your opponent into errors is certainly an aggressive play. The AM, strictly speaking, does not count net rushes, so it doesn't award players just for rushing the net. But the statisticians scoring the match, when they see a player make an error while attempting a passing shot, will score the error as forced. So when you calculate the Aggressive Margin, his opponent will be rewarded for forcing all those errors.

For AM purposes it doesn't matter whether a player was aggressive by rushing the net or by doing something else, like hitting a powerful forehand from the opposite baseline. As long as the resulting error is scored as forced, the player is rewarded and will generate a higher Aggressive Margin.

I think your analysis is quite interesting, but I disagree with the bolded statement. It also depends on what you define as peak. Are we referring to a period of time? ie. 2005-2006 for Federer. Or are we referring to peak levels in certain matches? If you are referring to peak level in certain matches, then that is fine, but players like Berdych, Tsonga and Del Potro will have very high margins for certain matches. If we are drawing a conclusion from the sample about a period of time, then there are some points to consider (see the reasons below).

To clarify, I don't think there is anything wrong with biasing towards more aggressive players since you are effectively trying to measure how aggressive a player relative to his/her errors.

Reasons for bias towards aggressive players:

1) Aggressive players play high risk high reward tennis, over the wide spread of matches played throughout one's career, they are more likely to have wins with a high margin of aggressively won points over unforced errors, than their defensive counterparts. This can cause skewed results. For example, let's say Isner and Nadal play 150 matches against the field during the defined "peak period" (150 matches is roughly 2-2.5 years).

Isner -Being a risky player, Isner always has a high winner/forced error, high unforced ratio. Over his 150 matches, his aggressive margin is 10%, because of his high unforced error count. However, he gets on fire 10 of the 150 (6.67%) matches he played, and has a high margin of 50% for his top 10 scores, supposedly representing his peak period.

Nadal -Being a defensive player, Nadal has a lower winner, lower unforced ratio. Over his 150 matches, his aggressive margin is 25%. Because of his steady play, this 25% held true for each of his 200 matches. Thus, his top 10 matches also average 25%, which is 1/2 of what Isner achieved in his top 10 matches.

This clearly does award players that "we normally think of as "an aggressive player."

To reduce this bias, perhaps one can define a peak period, say all matches in 2005 and 2006, and then select a random sample of matches to calculate the aggressive margin, rather than selecting the top aggressive margins over a large amount of years.

2) Also, using a direct calculation of % points won aggressively subtracting the % points lost due to unforced errors will be advantageous for the aggressive player.

ie: In a match, Isner won 50% of points aggressively, but lost 30% of points due to unforced errors. The aggressive margin is 20%. The RATIO is 50/30 = 1.67 times more aggressively won points than errors.

Nadal won 15% of points aggressively, but lost 2% of points due to unforced errors. The aggressive margin is 13%. The RATIO is 7.5 times more aggressively won points than errors.

Which statistic is actually more impressive in terms of "balancing aggressive shots and errors" as you said you were trying to find out from the stats?

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Some good points here. I think already, in my post to PC1, I addressed the arguments you make in your #2 section, concerning ratios vs margins. But I'll address your arguments specifically.

1) - you're talking about how high-risk players can get "hot" every once in a while and produce levels of play that more consistent players rarely, if ever, reach. That's an excellent point, and it certainly applies to players like Tsonga, Berdych, Isner.

However, it doesn't apply to Federer. No one, Nadal included, is more consistent than Federer. How many times is Federer upset in the early rounds of a tournament? Not often -- and it certainly has happened more frequently to Nadal, particularly in Slams. Federer may be high-risk if you look at his style in a certain way -- compared to Nadal, or Djokovic -- but his style is very far from hit-or-miss. And he doesn't have the temperamental psychology that makes some other players perform like a tennis god one day and then crap out the UE's in the next round.

When it comes to someone like Tsonga, no one doubts what you're saying. Tsonga's top AM's may exceed 40% or even 50% when his career is over, and those top figures might beat Nadal's top figures. But for average level of play, Nadal has Tsonga beaten hands down.

And you can see that illustrated very simply just by looking at their title count -- and the basic progress of their matches on tour. It's plain that Tsonga has more up-and-down days.

I just don't think the Nadal/Federer comparison works the same way. Federer has higher AM's. But it's not because he's a hot-and-cold player while Nadal is consistent. No one has been more consistent from day to day than Federer.

And you can see that in Federer's AM's. It's not just one or two AM's, like Tosnga produced on hot days, that are superior to Nadal's. Federer has several AM's over 40% (ABMK says he has Nadal at over 40% in one match); and Federer has several more in the high 30s, on my list, before Nadal's highest AM appears.

2) -- Here you're talking about how winner/error margins contrast with winner/error ratios. This was the question raised by PC1. He suggested that great, consistent defenders like Nadal might be better represented by ratios. I posted, in reply, several instances where Nadal comes out ahead of his opponent, if margins are used.

In short, Nadal does not win his matches by making 15 winners and 5 ue while his opponent (let's say it's Isner) makes 45 winners and 15 ue. Nadal can't win that match, because he's won only 30 points in total, while Isner has won 50. They might have same 3-to-1 ratio of winners/ue, but that's entirely inaccurate, given that Isner has probably won that match quickly in straight sets.

Your numbers are similar. You've got Isner already winning 50% of the points through his own aggressive plays. Plus he's taken 2% of the points through Nadal's unforced errors. So Isner has won 52% of the points in the match, at least; he has out-played Nadal, even if Nadal, as he sometimes does, steals the victory through mental or physical stamina when he has only won 48% of the points in the match.

Now, I'm not just being picky about the numbers you've chosen. I'm talking about which method is superior, as a way to measure quality of play. I'm saying, Isner has a higher Aggressive Margin than Nadal in this example, but that's entirely accurate, since Isner is out-playing Nadal. I'm also saying that, in your example, Nadal has the much higher RATIO of winners to errors: but that's entirely inaccurate as a measure of who is playing better. The ratio makes it seem that Nadal is playing entire levels above Isner, when in fact Rafa has been out-played in points won and will probably lose the match.

Your numbers don't quite add up to 100%, so I'll change them just a little.

Let's say Isner wins 48% of the points through his aggressive plays. He's also got 2% from Rafa's unforced errors. He's got 50% of the points. Nadal has won 15% of the points aggressively, and 35% from Isner's unforced errors.

Each man is tied in total points won, so we have a fair playing field to decide which method is better.

Isner's Aggressive Margin is 48% - 35%, or 13%. Nadal's AM is 15% - 2%, or 13%. That's a precise representation of the distance between the two men.

I had never noticed it before, but the Aggressive Margin will always tell you accurately which player won the most points. It's tied in mathematically to the breakdown of Total Points Won. I tried it in Excel today, punching in various numbers for Unforced Errors to see if I could get Isner and Nadal to produce the numbers that you gave them. It turns out that you can put in any numbers you want, for the Unforced Errors; it doesn't matter; if Nadal and Isner have won the same number of points, their Aggressive Margins will be equal to one another. If Isner wins 90 points and Nadal 89, Isner's AM will be slightly higher than Nadal's. It has to work out that way mathematically.

Try it out in Excel. You can give Isner 145 unforced errors, and Nadal only 2; or you can give them both 40 unforced errors; the particular figures don't matter. The player's AM's will always reflect the actual margin of victory in Total Points Won.

What the exact AM's will be, of course, is totally dependent on how many UE's the players make. The actual UE figures determine the quality of the AM's.

But the AM's always accurately represent who won the most points, and by how much. I'm not sure any method can hope to be more fair than that.

Because I have all this data in Excel, I can easily sort by different criteria and compare different methods. I took all my data today and sorted it by ratios, rather than by Aggressive Margins. The ratios end up distorting a lot; but I'll put that it another post.

Yes those official stats are messed up, but fortunately they don't have an impact on the AM. As long as the unforced errors can be trusted -- and they do look ok -- then the remaining points can be regarded as either forcing points or as clean winners, without worrying about how many exactly were clean winners. That's the problem with the official stats: the figures that they have for Winners are actually the number of points that each player won, in total, on serve (ie, Federer won 31 points on his own serve, Nadal won 46 on his own).

In 2007 the RG site also had a problem counting Winners, and I don't know how the Winners were calculated that year. Fortunately, again, it doesn't have an impact on the AM, so long as the Unforced Errors look reliable, which they do.

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the unforced errors column *may* be ok ... I counted 17 UEs for federer ( they had 12 ) and 4 UEs for nadal ( they had 3 ) in the first set ... Maybe I was a bit harsher in evaluating UEs, whereas the statistician was a bit more lenient or a combination of the 2 ....

The official Wimbledon stats in '99 have Unforced Errors that are completely unreliable. Those figures look like the total number of errors of every kind, forced and unforced. They've got Sampras at 51 unforced errors. NBC put Sampras at only 22, which looks right. Unfortunately I don't know the UE count that NBC had for Agassi, so AM's can't be calculated.

Do you have any idea what the UE counts were for the Stich match?

Or the UE count for Becker in the '95 Wimby final?

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I don't have the UE stats for either of the matches.

yeah, I did see the stats for the wimbledon 99 final .. looks like they combined forced and unforced errors as 'unforced errors'.

do you have the UE counts for the krajicek-sampras match in 96 ? I saw the huge boxscore on the site, some really really detailed stats, but sadly can't get the total UE count from there !

Some good points here. I think already, in my post to PC1, I addressed the arguments you make in your #2 section, concerning ratios vs margins. But I'll address your arguments specifically.

1) - you're talking about how high-risk players can get "hot" every once in a while and produce levels of play that more consistent players rarely, if ever, reach. That's an excellent point, and it certainly applies to players like Tsonga, Berdych, Isner.

However, it doesn't apply to Federer. No one, Nadal included, is more consistent than Federer. How many times is Federer upset in the early rounds of a tournament? Not often -- and it certainly has happened more frequently to Nadal, particularly in Slams. Federer may be high-risk if you look at his style in a certain way -- compared to Nadal, or Djokovic -- but his style is very far from hit-or-miss. And he doesn't have the temperamental psychology that makes some other players perform like a tennis god one day and then crap out the UE's in the next round.

When it comes to someone like Tsonga, no one doubts what you're saying. Tsonga's top AM's may exceed 40% or even 50% when his career is over, and those top figures might beat Nadal's top figures. But for average level of play, Nadal has Tsonga beaten hands down.

And you can see that illustrated very simply just by looking at their title count -- and the basic progress of their matches on tour. It's plain that Tsonga has more up-and-down days.

I just don't think the Nadal/Federer comparison works the same way. Federer has higher AM's. But it's not because he's a hot-and-cold player while Nadal is consistent. No one has been more consistent from day to day than Federer.

And you can see that in Federer's AM's. It's not just one or two AM's, like Tosnga produced on hot days, that are superior to Nadal's. Federer has several AM's over 40% (ABMK says he has Nadal at over 40% in one match); and Federer has several more in the high 30s, on my list, before Nadal's highest AM appears.

2) -- Here you're talking about how winner/error margins contrast with winner/error ratios. This was the question raised by PC1. He suggested that great, consistent defenders like Nadal might be better represented by ratios. I posted, in reply, several instances where Nadal comes out ahead of his opponent, if margins are used.

In short, Nadal does not win his matches by making 15 winners and 5 ue while his opponent (let's say it's Isner) makes 45 winners and 15 ue. Nadal can't win that match, because he's won only 30 points in total, while Isner has won 50. They might have same 3-to-1 ratio of winners/ue, but that's entirely inaccurate, given that Isner has probably won that match quickly in straight sets.

Your numbers are similar. You've got Isner already winning 50% of the points through his own aggressive plays. Plus he's taken 2% of the points through Nadal's unforced errors. So Isner has won 52% of the points in the match, at least; he has out-played Nadal, even if Nadal, as he sometimes does, steals the victory through mental or physical stamina when he has only won 48% of the points in the match.

Now, I'm not just being picky about the numbers you've chosen. I'm talking about which method is superior, as a way to measure quality of play. I'm saying, Isner has a higher Aggressive Margin than Nadal in this example, but that's entirely accurate, since Isner is out-playing Nadal. I'm also saying that, in your example, Nadal has the much higher RATIO of winners to errors: but that's entirely inaccurate as a measure of who is playing better. The ratio makes it seem that Nadal is playing entire levels above Isner, when in fact Rafa has been out-played in points won and will probably lose the match.

Your numbers don't quite add up to 100%, so I'll change them just a little.

Let's say Isner wins 48% of the points through his aggressive plays. He's also got 2% from Rafa's unforced errors. He's got 50% of the points. Nadal has won 15% of the points aggressively, and 35% from Isner's unforced errors.

Each man is tied in total points won, so we have a fair playing field to decide which method is better.

Isner's Aggressive Margin is 48% - 35%, or 13%. Nadal's AM is 15% - 2%, or 13%. That's a precise representation of the distance between the two men.

I had never noticed it before, but the Aggressive Margin will always tell you accurately which player won the most points. It's tied in mathematically to the breakdown of Total Points Won. I tried it in Excel today, punching in various numbers for Unforced Errors to see if I could get Isner and Nadal to produce the numbers that you gave them. It turns out that you can put in any numbers you want, for the Unforced Errors; it doesn't matter; if Nadal and Isner have won the same number of points, their Aggressive Margins will be equal to one another. If Isner wins 90 points and Nadal 89, Isner's AM will be slightly higher than Nadal's. It has to work out that way mathematically.

Try it out in Excel. You can give Isner 145 unforced errors, and Nadal only 2; or you can give them both 40 unforced errors; the particular figures don't matter. The player's AM's will always reflect the actual margin of victory in Total Points Won.

What the exact AM's will be, of course, is totally dependent on how many UE's the players make. The actual UE figures determine the quality of the AM's.

But the AM's always accurately represent who won the most points, and by how much. I'm not sure any method can hope to be more fair than that.

Because I have all this data in Excel, I can easily sort by different criteria and compare different methods. I took all my data today and sorted it by ratios, rather than by Aggressive Margins. The ratios end up distorting a lot; but I'll put that it another post.

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Ah, I see thanks for the clarification! For point 1, I was under the impression that this was just used to measure all players across the board, but I guess you also took into consideration the consistency of Fed/Nadal specifically.

And for point two I thought you meant % of aggressive points won as in aggressive points divided by total points won by the specific player, rather than divided by the total points in the match, so that's why there's that confusion there too (ie. not adding up to 100% for Isner and Nadal's points won).

But ya, thanks for going through the analysis and answering my post! Too often my posts on this forum get overshadowed because the OP is too busy defending against troll posts LOL!

You know, that's my favorite match, yet in all this talk about aggressive play I had actually forgotten about Wilander's net rushes. We typically think of aggression as hitting winners, but in past eras "aggressive" meant rushing the net! Absolutely right.

Wilander had, I think, 131 approaches, Lendl 77. Lendl was aggressive, too, by that measure -- more than most players today. But Wilander was twice as willing to come forward.

That was part of the reason that Lendl hit so many more winners: Wilander forced him to hit a ton of passing shots.

You ask if we can take passing shot errors into account. Rushing the net and forcing your opponent into errors is certainly an aggressive play. The AM, strictly speaking, does not count net rushes, so it doesn't award players just for rushing the net. But the statisticians scoring the match, when they see a player make an error while attempting a passing shot, will score the error as forced. So when you calculate the Aggressive Margin, his opponent will be rewarded for forcing all those errors.

For AM purposes it doesn't matter whether a player was aggressive by rushing the net or by doing something else, like hitting a powerful forehand from the opposite baseline. As long as the resulting error is scored as forced, the player is rewarded and will generate a higher Aggressive Margin.

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It's funny, that could be my favorite match too along with the 1984 Connors/McEnroe US Open semi and a couple of others. I play the 1988 US Open final as background video often on the TV or computer monitor when I'm doing some paperwork.

Ah, I see thanks for the clarification! For point 1, I was under the impression that this was just used to measure all players across the board, but I guess you also took into consideration the consistency of Fed/Nadal specifically.

And for point two I thought you meant % of aggressive points won as in aggressive points divided by total points won by the specific player, rather than divided by the total points in the match, so that's why there's that confusion there too (ie. not adding up to 100% for Isner and Nadal's points won).

But ya, thanks for going through the analysis and answering my post! Too often my posts on this forum get overshadowed because the OP is too busy defending against troll posts LOL!

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Ok no prob.

Yeah, that's one reason I prefer posting in this sub-forum even when mostly talking about current players (but at some point in this thread hopefully we can talk more about former players' stats).

Yesterday we were debating whether to use margins or ratios. We talked a lot about winner/error ratios, but I wondered what would happen if I used the broader category of Aggressive Points rather than just the Winners that are usually reported in the media. Aggressive Points are all the points a player wins either by striking clean winners or forcing his opponent into errors.

Above are the resulting ratios for Nadal and Federer and Wimbledon. For example, in the 2006 final, Federer's Aggressive Points were 3.34 times more numerous than his unforced errors.

But the ratios do not reflect the results accurately. Federer's ratio is just slightly better than Nadal's in 2006, implying a tight victory, when in fact it was a four-setter.

Nadal barely won the 2008 match, 9-7 in the fifth, but his ratio is much larger than Federer's, implying an easy victory.

Finally in 2007, Nadal lost the match but he has a higher ratio than Federer.

When I sorted all my data in Excel according to ratios, some strange things came up.

The best example is Wilander's five-set loss to Sampras at the 1989 USO. Wilander had an Aggressive Margin of 29.8%. That was #74 among all the AM's I had calculated, that is, the 74th highest AM.

But when ratios are used, Wilander's performance jumps to the 5th best performance in all my data. His ratio of Aggressive Points to UE is 12.38. It's not only better than Sampras' performance in the same match (Pete drops down to #110 on the list, with a ratio of just 2.88 ). Wilander's performances also looks better, by this measure, than any performance by Federer, Sampras, Nadal or Djokovic.

The reason is that Wilander made only 8 unforced errors in that match. Nobody was better at keeping his unforced errors down.

And if you have your UE's down in the single digits, you're going to generate extremely high ratios of Aggressive Points to UE's. It's easy to see why: if you make 50 Aggressive Points and 2 UE's, your ratio is 25.0. Drop down just 1 UE, and your ratio jumps to 50.0.

Sampras/Wilander was the most extreme example, but there were others. It's clear that ratios disproportionately favor great defenders, and give inaccurate pictures of results.

The Aggressive Margin, by contrast, has Sampras at 31.5%, Wilander at 29.8%, an accurate representation of Pete's narrow five-set victory.

Anyway, I'll get back to posting more AM's -- I have several more now, including some very high ones for Nadal.

That's right, Courier had a negative AM against Bruguera (though he's not the only player I've had negative numbers for).

That basically means he the cost he paid in unforced errors was greater than what he was able to win through aggressive plays.

But Bruguera's AM was not much higher. On clay this should not be that much of a surprise.

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But it does suggest a lower level of play than in more recent finals, where AM's have been in the 20s-30s, correct?

Also, Brignacca provides the average AM's for the 2005 Grand Slams in the paper you linked in the OP. For men, he has them as follows.

Australian 22.5%
French 10.7%
Wimbledon 29.0%
USO 22.1%

Would it be fair or proper to add or subtract a surface factor when comparing performances in matches played on different surfaces? For example, Rafa's AM in the 2008 RG final was 34.7%, but that might equate to a 53.0% performance at Wimbledon if we added the difference between the French and Wimbledon AM averages.